Create all possible words using a set or letters

Question

Given a list of letters,

letters = { "A", "B", ..., "F" }

is it possible to get Mathematica to generate all ‘words’ (in this example, 6 letter words), if only one letter can be used one time only, e.g. ABCDEF, ABCDFE, …? TIA.

Answer 1

Pemutations will do it:

letters = {"a", "b", "c"};
Permutations[letters, {3}]
{{"a", "b", "c"}, {"a", "c", "b"}, {"b", "a", "c"}, 
 {"b", "c", "a"}, {"c", "a", "b"}, {"c", "b", "a"}}

To get all six-letter words:

letters = {"a", "b", "c", "d", "e", "f"};
perms = Permutations[letters, {6}];
StringJoin /@ perms

{"abcdef", "abcdfe", "abcedf", "abcefd", "abcfde" ... etc.

there are a lot of them.

Answer 2

You can create permutations with all of the letters as strings with:

StringJoin /@ Permutations[letters]

If you want lists of the individual letters just use:

Permutations[letters]

Check the documentation of Permutations to learn about permutations with subsets of letters. If you want to use each letter more than once, look at the documentation for Tuples.

Answer 3

If I follow the OP's question, I think they want the following:

letters = {"a", "b", "c"};
p = Permutations[letters, {#}] & /@ Range[Length[letters]];
(StringJoin[#] & /@ #) & /@ p

{{a, b, c}, {ab, ac, ba, bc, ca, cb}, {abc, acb, bac, bca, cab, cba}}